e_pas for every compartment set to -112.55mV in the model!!!
I just ran the H_current.hoc file in the model given at modeldb: https://senselab.med.yale.edu/modeldb/s ... 212#tabs-1
When I printed e_pas using the following command in hoc: soma[0].e_pas(0.5) , It showed -112.55mV. I know this was done by the current-balance.hoc file to initialize the model to v_init, but this seems unphysiological.

Furthermore, if you calculate the input capacitance (current calmp of 10pA at soma, then calculate input resistance - ~65Mohms and tau - ~15ms. Then calculated Cm), it's coming out to be 420pF!! (Neuroelectro and my in-lab data says it should be around 65pF)
Can anybody help me with this?

initialize the model to v_init
for each compartment in the model
calculate the local net ionic membrane current
add a local constant membrane current of equal magnitude but opposite sign

Since net membrane current will then be 0 when membrane potential equals v_init, the result is a model with a resting potential of v_init.

One way to accomplish this result would be to insert into all sections a density mechanism that delivers a constant current, and adjust the value of this current in each compartment to force local charge balance.

The authors of the model you cite accomplished the same result by taking advantage of the fact that every compartment in their model had a mechanism with a linear constant conductance (the pas mechanism, in this particular case). Then they probably did something equivalent to

initialize the model to v_init
for each compartment in the model
calculate the sum of all local ionic membrane currents EXCEPT i_pas
set local e_pas to a value that makes local i_pas equal to -1 times that sum

I wrote "probably" because I haven't checked their rather obfuscated code to discover what they did, or verify that they did it correctly.

"Can you prove that this second approach, i.e. changing e_pas in each compartment, is equivalent to the first approach, i.e. adding a constant current to each compartment?"

Yes. Consider the model with unperturbed e_pas. The equivalent circuit for each compartment includes a branch with voltage source e_pas in series with a conductance g_pas

(the little o's are the terminals of this branch)
which can be analyzed like any other single port linear circuit. In particular, it has an open circuit voltage, a closed circuit current, and a source resistance, the values of which are e_pas, g_pas*e_pas, and 1/g_pas, resepectively.

Now consider the model with perturbed e_pas. The equivalent circuit for each compartment has a branch with voltage source e_pas+delta in series with conductance g_pas

with a current source of magnitude g_pas*delta. Why? Its open circuit voltage is e_pas + delta, its closed circuit current is g_pas*(e_pas + delta), and its source resistance is 1/g_pas. So tweaking e_pas by some amount delta is equivalent to leaving e_pas unchanged while attaching a current source of magnitude g_pas*delta.

if you calculate the input capacitance (current calmp of 10pA at soma, then calculate input resistance - ~65Mohms and tau - ~15ms. Then calculated Cm), it's coming out to be 420pF!! (Neuroelectro and my in-lab data says it should be around 65pF)

Good question. Experimental measurements are prone to all kinds of vagaries, and so is computational modeling. Did Poirazi et al. say where they got the anatomical and biophysical data on which they based their model? What species were used, what were the ages of the animals? What about for the data you found in NeuroElectro? Were the experiments done in slices, and if so, were the dendritic trees intact?